Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class ProblemF {

    public static InputStream inputStream = System.in;

    public static OutputStream outputStream = System.out;

    public static void main(String[] args) {
        MyScanner scanner = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int n = scanner.nextInt();

        Tree tree1 = new Tree(n);
        Tree tree2 = new Tree(n);
        Tree tree3 = new Tree(n);
        for (int i = 0; i < n - 1; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            tree1.addEdge(x, y);
            tree2.addEdge(x, y);
            tree3.addEdge(x, y);
        }

        int s = 0;

        tree1.makeTree(1);
        tree1.bfs(Collections.singletonList(1));
        int x = tree1.getFarthestNode();

        tree2.makeTree(x);
        tree2.bfs(Collections.singletonList(x));
        int y = tree2.getFarthestNode();
        s += tree2.nodes.get(y).dist;
        if (s == n) {
            out.println(n - 1);
            out.print(x + " " + y + " ");
            for (int i = 1; i <= n; i++) {
                if (i != x && i != y) {
                    out.print(i);
                    break;
                }
            }
        } else {
            List<Integer> list = new ArrayList<>();
            Node yNode = tree2.nodes.get(y);
            while (yNode != null) {
                list.add(yNode.label);
                yNode = yNode.adj;
            }

            tree3.makeTree(y);
            tree3.bfs(list);
            int z = tree3.getFarthestNode();
            s += tree3.nodes.get(z).dist - 1;

            out.println(s - 1);
            out.println(x + " " + y + " " + z);
        }


        out.flush();
    }

    private static class Tree {

        private Node root;

        private Map<Integer, Node> nodes = new HashMap<>();

        private Tree(int n) {
            for (int i = 1; i <= n; i++) {
                nodes.put(i, new Node(i));
            }
        }

        private void addEdge(int x, int y) {
            nodes.get(x).addChild(nodes.get(y));
            nodes.get(y).addChild(nodes.get(x));
        }

        private void makeTree(int rootLabel) {
            root = nodes.get(rootLabel);
            root.makeTree(rootLabel);
        }

        private void bfs(List<Integer> initialNodes) {
            LinkedList<Node> toVisit = new LinkedList<>();
            for (int x : initialNodes) {
                Node node = nodes.get(x);
                node.dist = 1;
                toVisit.add(node);
            }

            while (!toVisit.isEmpty()) {
                Node node = toVisit.poll();
                for (Node child : node.children) {
                    if (child.dist == 0) {
                        child.dist = node.dist + 1;
                        toVisit.add(child);
                        child.adj = node;
                    }
                }
            }
        }

        private int getFarthestNode() {
            int x = 1;
            for (int i = 2; i <= nodes.size(); i++) {
                if (nodes.get(i).dist > nodes.get(x).dist) {
                    x = i;
                }
            }
            return x;
        }
    }

    private static class Node {

        private int label;

        private int dist;

        private List<Node> children = new ArrayList<>();

        private Node adj;

        private Node(int label) {
            this.label = label;
        }

        private void addChild(Node child) {
            children.add(child);
        }

        private void makeTree(int parent) {
            for (Node child : new ArrayList<>(children)) {
                if (child.label == parent) {
                    children.remove(child);
                } else {
                    child.makeTree(this.label);
                }
            }
        }
    }

    private static class MyScanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        private MyScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private String next() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private double nextDouble() {
            return Double.parseDouble(next());
        }

        private String nextLine() {
            String str = "";
            try {
                str = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    private static class Pair<F, S> {

        private F first;

        private S second;

        public Pair() {
        }

        public Pair(F first, S second) {
            this.first = first;
            this.second = second;
        }
    }
}